Question

Quadrilateral ABCD has the following vertices: A(-4, -4), B(2, -4), C(4, -7), and D(-3, -7). Quadrilateral ABCD is a:

a. Square
b. Rectangle
c. Parallelogram
d. Rhombus

Answer 1

Based on calculating the distances between the vertices, quadrilateral ABCD with vertices A(-4, -4), B(2, -4), C(4, -7), and D(-3, -7) is best classified as a parallelogram, since the opposite sides are equal in length.

Step-by-step explanation:

The student has asked a mathematical question regarding the classification of a quadrilateral with specified vertices. To determine the type of quadrilateral ABCD with vertices A(-4, -4), B(2, -4), C(4, -7), and D(-3, -7), we need to calculate the distances between each pair of adjacent vertices and check for equal side lengths and angles. Upon calculation, we discover:

• The distance between A and B is 6 units.
• The distance between B and C is approximately 3.61 units (using the distance formula).
• The distance between C and D is 7 units.
• The distance between D and A is also approximately 3.61 units.

Since the opposite sides AB and CD are not equal in length, nor are AD and BC, this indicates that ABCD is not a square, rectangle, or rhombus. Therefore, the correct classification based on this information is that ABCD is a parallelogram, as only opposite sides are required to be equal in length for a quadrilateral to be classified as such.